In these lectures I will discuss the properties of functionals of onedimensional Brownian motion. These lectures will aim to provide a pedagogical introduction to the path integral methods leading to the derivation of the celebrated Feynman-Kac formula. The usefulness of this technique in calculating the statistical properties of Brownian functionals will be illustrated with several examples in physics and probability theory, with particular emphasis on applications in computer science. The statistical properties of first-passage Brownian functionals and their applications will also be discussed. These lectures are organized jointly with the “Ecole Doctorale de Physique de la region Parisienne (ED107)”

LPTMS, Université Paris XI, Orsay